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中文摘要：
针对非线性系统的随机性的特点，提出了随机非线性系统自由状态方程的任意阶近似解法．该解法从自由状态空间中的广义朗之万梯度方程出发，利用常数变易法导出了与广义朗之万方程等价的广义的第二类非线性、随机性Valterra积分方程，采用逐次逼近法求得了方程的任意阶近似解．最后，讨论了非线性、随机性对系统状态空间转移的影响．随机非线性系统自由状态方程的任意阶近似解法为随机非线性系统的定量分析提供了一种有效方法．
英文摘要：
Armed at the difficult solution of uncontrolled random nonlinear systems,a method for any order approximate solution of the state equation for uncontrolled random nonlinear systems is proposed. Based on general Langevin gradient equation in uncontrolled state space, the random nonlinear Volterra＇s integral equation for the second kind, which is equivalent to general Langevin gradient equation, is obtained, by utilizing constant variation method. Then, any order approximate solution of the equation is also obtained, by successive approximation method. Finally, the influences of nonlinearity and randomness for state space transformation of the system is discussed. The method for any order approximate solution of the state equation for uncontrolled random nonlinear systems is an effective method of quantitative analysis for random nonlinear systems.
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